When we get to the end of a string, the automata is either in an accepting state or not. If that ain't a boolean, it'll do till one comes along...at least for me as I have a hard time imagining uses for regular expressions that aren't implemented so as to return values. Then again I'm not that bright and tend to mumble along writing down my thoughts.
Which is why I'm writing about types...it seems to unroll the at hand possible "compatible/incompatible" conundrum of the name...or at least when after writing about it and heaedd to bed, I realized a simpler illustration was possible using Sets...and isn't that just the way of the maths, one description is isomorphic with another that makes explanation easier? Alas, I despaired of sharing it, but then this very morning I found a place for it.
Anyway, if one tests for compatibility [whatever that may be] between a set S and a superset SS as suggested above, the results of the test depend on both the test chosen and the ordering of the arguments. This is to say:
For each m in S, m is member of SS -> true
For each mm in SS, mms is member if S -> false
But choosing a different test
S is subset of SS -> true
SS is subset of S -> false
Of course whether we map true to compatibility [whatever that is] or incompatibility is entirely dependent in our arbitrary choice of whether our test is deemed to be for compatibility or incompatibility.
I wish I had an easy answer, but it's turtles, even by any other sweet smelling name, all the way down I'm afraid.
Which is why I'm writing about types...it seems to unroll the at hand possible "compatible/incompatible" conundrum of the name...or at least when after writing about it and heaedd to bed, I realized a simpler illustration was possible using Sets...and isn't that just the way of the maths, one description is isomorphic with another that makes explanation easier? Alas, I despaired of sharing it, but then this very morning I found a place for it.
Anyway, if one tests for compatibility [whatever that may be] between a set S and a superset SS as suggested above, the results of the test depend on both the test chosen and the ordering of the arguments. This is to say:
But choosing a different test Of course whether we map true to compatibility [whatever that is] or incompatibility is entirely dependent in our arbitrary choice of whether our test is deemed to be for compatibility or incompatibility.I wish I had an easy answer, but it's turtles, even by any other sweet smelling name, all the way down I'm afraid.